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Question

Co-efficient of linear expansion of brass and steel rods are α1 and α2 respectively. Lengths of brass and steel rods are L1 and L2 respectively. If (L2L1) is maintained same at all the temperatures, which one of the following relations holds good?

A
α1L1=α2L2
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B
α1L2=α2L1
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C
α1L22=α2L21
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D
α21L2=α22L1
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Solution

The correct option is A α1L1=α2L2
As per the question, L2L1= constant
Let L1 and L2 be the lengths of the rods when temperatures are changed.
L2L1=L2L1
L2(1+α2ΔT)L1(1+α1ΔT)=L2L1
[ temperature change will be same for both the rods ]
L2α2=L1α1

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